4. Suppose your prior distribution for θ the proportion of Iowans who support the death penalty, ...
4. Suppose your prior distribution for θ the proportion of Iowans who support the death penalty, is beta with mean 0.60 and standard deviation 0.30. (a) Determine the parameters a and B of your prior distribution. Sketch the prior density function Feel free to use the following R code theta seqC0,1,.001) dens <- dbeta(theta,1,.67) plot (theta, dens, xlim-co,1), ylim-c(0,3), type-"1", xlab-"theta") (b) A random sarnple of 1,000 Iowans is taken, and 65% support the death penalty. What are your posterior mean and variance for θ? Sketch the posterior density. c) Examine the sensitivity of the posterior distribution to different prior means and standard dev ations
4. Suppose your prior distribution for θ the proportion of Iowans who support the death penalty, is beta with mean 0.60 and standard deviation 0.30. (a) Determine the parameters a and B of your prior distribution. Sketch the prior density function Feel free to use the following R code theta seqC0,1,.001) dens